Ethereal Forager

• WOTC Official Reminder Textofficial rules
  Delve — Each card you exile from your graveyard while casting this spell pays for .

• WWizards of the Coast2020-04-17
  Official Ruling
  If Ethereal Forager leaves the battlefield while its triggered ability is on the stack, that ability can still find the cards exiled with Ethereal Forager’s delve ability.
• WWizards of the Coast2020-04-17
  Official Ruling
  After Ethereal Forager’s triggered ability resolves, players will have priority to cast spells (such as the card you returned to your hand, if it’s legal to do so) before blockers are declared.
• WWizards of the Coast2021-03-19
  Official Ruling
  Because delve isn’t an alternative cost, it can be used in conjunction with alternative costs, such as flashback. It can also be used to pay for additional costs that include generic mana.
• WWizards of the Coast2021-03-19
  Official Ruling
  You can exile cards to pay only for generic mana, and you can’t exile more cards than the generic mana requirement of a spell with delve. For example, you can’t exile more than seven cards from your graveyard to cast Treasure Cruise unless an effect has increased its cost.
• WWizards of the Coast2021-03-19
  Official Ruling
  Delve doesn’t change a spell’s mana cost or mana value. For example, Treasure Cruise’s mana value is 8 even if you exiled three cards to cast it.

Rulings via Scryfall